Question: Solve for $x$ and $y$ using elimination. ${3x-4y = -22}$ ${-4x+3y = 6}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $4$ and the bottom equation by $3$ ${12x-16y = -88}$ $-12x+9y = 18$ Add the top and bottom equations together. $-7y = -70$ $\dfrac{-7y}{{-7}} = \dfrac{-70}{{-7}}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {3x-4y = -22}\thinspace$ to find $x$ ${3x - 4}{(10)}{= -22}$ $3x-40 = -22$ $3x-40{+40} = -22{+40}$ $3x = 18$ $\dfrac{3x}{{3}} = \dfrac{18}{{3}}$ ${x = 6}$ You can also plug ${y = 10}$ into $\thinspace {-4x+3y = 6}\thinspace$ and get the same answer for $x$ : ${-4x + 3}{(10)}{= 6}$ ${x = 6}$